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(CNN)Donald Trump is facing a critical test in the final six weeks of the primary season: securing the 1,237 delegates needed to finally claim the Republican presidential nomination as his own.

The prospect of a historic contested convention has surrounded Trump's candidacy for months. But Trump is much closer to winning the nomination outright following his resounding victories in Tuesday's East Coast primaries, which boosted his delegate count to at least 988 compared to 568 for his chief rival, Ted Cruz.

Trump needs to win 49% of the remaining Republican delegates to capture the nomination, according to CNN estimates. He's been winning delegates so far at a rate of 49%, making that target well within reach.

Still, he is facing headwinds as the primary calendar winds down: both in the newly forged alliance between Cruz and Ohio Gov. John Kasich and the complex political terrain in Indiana and California will determine whether Trump can win the nomination outright. Cruz is also making a last-ditch effort to revitalize his campaign by saying Wednesday that Carly Fiorina would be his running mate if he won the GOP nomination.

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Major contests

The major primary contests will be more spread out over the next month as the primary calendar expands west to Indiana, Nebraska, Oregon and Washington State before culminating in the June 7 contests that include New Mexico, New Jersey and California.

It is unclear, however, whether Trump's team has built the organization to pull off the kinds of margins that he will need in logistically complex states like California—where the candidates are competing for 172 delegates in 53 different congressional districts.

Despite leadership changes in his campaign and the expansion of his once skeletal staff, Trump's campaign has been repeatedly outmatched by Cruz's superior organization in the parallel campaign to identify, vet and elect loyal delegates who would stand by him through successive rounds of ballots at an open convention if Trump didn't clinch the support of 1,237 delegates on the first ballot.

At the same time, it is too early to tell whether the Cruz-Kasich gambit to split up Indiana, Oregon and New Mexico—essentially agreeing not to compete against one another in those states—will succeed or backfire, particularly at a time when many Republican voters are demonstrating their frustration with GOP establishment at the ballot box.

"Strategic voting and strategic campaigning is the only way to keep him from reaching 1,237," said South Carolina Sen. Lindsey Graham, an ardent Trump critic who is backing Cruz. The question is whether "it will be clear to Kasich people in Indiana that they have to vote for Cruz to stop Trump," he said.

"If they can execute this," Graham said, "I think it stops him."

Trump argued Tuesday night that the alliance is just another sign of his rivals' "tremendous weakness" and the establishment's collusion against him.

"I consider myself the presumptive nominee," Trump said in his victory speech in New York.

"It's over," he said, stating that Cruz and Kasich made a mistake with their "faulty deal."

Different strategies

Trump and Cruz demonstrated their starkly different strategies for this closing stretch of the race on Wednesday.

Trump, who has been striving to appear more presidential, delivered a blistering attack of President Barack Obama's foreign policy during a formal speech in Washington.

In an effort to improve his standing among Republicans and party elites who question his credentials to be President, Trump adopted a serious tone as he outlined his foreign policy views and said the "overriding theme" of his administration would be putting American interests first.

Cruz, by contrast, adopted an almost-Trump-like tactic to try to regain control of the news cycle after his bruising losses Tuesday night. He announced at an afternoon event in Indianapolis that if he were nominated, he would choose Fiorina, the former Hewlett-Packard CEO, as his running mate.

The splashy announcement was intended to give a much needed jolt of energy to his campaign — amplifying his argument that he would be better suited to take on Hillary Clinton, particularly with Fiorina at his side.

In the near term, Cruz is pinning his hopes squarely on next week's contest in Indiana. Before Trump's East Coast wins had even been called on Tuesday night, Cruz predicted that "the media" would say "the race is over" and that "Donald Trump is the Republican nominee."

But the Texas senator pointed to his prospects in western states beyond Indiana — Nebraska, North Dakota, Montana, Washington and California — as spots where he could slow down Trump's momentum.

Cruz clearly hopes that asking Fiorina to join his potential ticket will give him an added boost in California, where Fiorina unsuccessfully ran for a U.S. Senate seat against Barbara Boxer in 2010. Though Fiorina was popular among Republicans in California, she was widely viewed as a flawed candidate because of her mixed business record at HP, which also became a liability in her recent presidential campaign.

The anti-Trump forces have signaled vigorous efforts ahead to try to weaken Trump in Indiana and California. The anti-Trump Our Principles PAC dismissed the real estate magnate's wins on Tuesday as "neither surprising nor decisive" in a strategy memo. They are also eyeing opportunities in Montana and South Dakota, where there could be opportunities to peel off delegates from Trump.

"We're rolling on to Indiana and other states out west in May and June, and we fully intend to fight for every last delegate," said Brian Baker, a senior advisor to Our Principles PAC.

Fresh burst of momentum

But with some donors waiting to see if Trump can get build a fresh burst of momentum in Indiana, it is unclear whether the assorted anti-Trump groups can raise enough money to beat back Trump in a state like California. A Fox News poll released last week showed Trump with a double digit lead over both Cruz and Kasich in California.

Trump's advisers have already signaled their intentions to make a major push in California, where results are winner-take-all in each of the state's 53 congressional districts. Because of his personal wealth, Trump could potentially have the resources to commit to statewide media buys that can cost between $2.5 million and $3 million a week.

But once again, Trump's campaign is up against a devoted and well-organized effort by Cruz, who has been identifying and recruiting potential delegates in the Golden State for a better part of a year.

Kasich may be able to peel off some delegates by targeting some of the moderate congressional districts in the Bay Area where he will campaign on Friday, but the candidates will essentially be competing in 53 mini-contests across the vast geography of the state.

"We have as close to a pure democracy as you can get," California Republican Party Chairman Jim Brulte said in an interview, pushing back on the notion that California poses a daunting challenge to campaigns that are already stretched thin.

In a sign that his campaign is stepping up their strategic game, Trump will appear at the California GOP convention later this week, in the hopes of swaying some potential delegates. Cruz, Kasich and Fiorina will all speak at this weekend's gathering in the Bay Area.

Last week, Trump also dispatched a robocall to independent voters across California—who are technically classified as "no party preference"—urging them to register with the Republican Party so they can participate in the closed primary on June 7. So far there has been no noticeable surge in registration changes with the Secretary of State's office, but that could change as the deadline to change parties approaches on May 23.

The question now is whether Cruz and Kasich's shaky alliance will extend to the Golden State. That's under discussion, one Kasich operative acknowledged, but no deal has been struck yet.

Update: This post has been updated with new information to reflect the correct percent of remaining delegates Trump needs to win.